#include <Eigen/Sparse>
#include <iostream>
#include <vector>

typedef Eigen::SparseMatrix<double> SpMat; // declares a column-major sparse matrix type of double
typedef Eigen::Triplet<double> T;

void
buildProblem(std::vector<T>& coefficients, Eigen::VectorXd& b, int n);
void
saveAsBitmap(const Eigen::VectorXd& x, int n, const char* filename);

int
main(int argc, char** argv)
{
	if (argc != 2) {
		std::cerr << "Error: expected one and only one argument.\n";
		return -1;
	}

	int n = 300;   // size of the image
	int m = n * n; // number of unknowns (=number of pixels)

	// Assembly:
	std::vector<T> coefficients; // list of non-zeros coefficients
	Eigen::VectorXd b(m);		 // the right hand side-vector resulting from the constraints
	buildProblem(coefficients, b, n);

	SpMat A(m, m);
	A.setFromTriplets(coefficients.begin(), coefficients.end());

	// Solving:
	Eigen::SimplicialCholesky<SpMat> chol(A); // performs a Cholesky factorization of A
	Eigen::VectorXd x = chol.solve(b);		  // use the factorization to solve for the given right hand side

	// Export the result to a file:
	saveAsBitmap(x, n, argv[1]);

	return 0;
}
